Question 7
A triangle has sides of length $x,y,20$ where $x\gt y\gt 20$ and $x,y$ are integers. Let $h$ be the length of the altitude of the triangle from the side of length 20. Let $h_x,h_y$ be the lengths of the altitudes from the sides of length $x,y$ respectively. These altitudes satisfy $h=h_x+h_y$. Find the perimeter of this triangle.
Numerical answer only; a non-negative integer less than 1000.
Numerical answer only; a non-negative integer less than 1000.